ubiquitous & mobile computing
TRANSCRIPT
Copyrighted material; for CBU ICT Summer School 2009 student use only
Technische Universität Darmstadt
Telecooperation
Ubiquitous & Mobile ComputingConnectivity: Mobile Networks 1
Dr. Erwin Aitenbichler
Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
General Introduction – Connectivity
• Background: Elaborate Disciplines of– Computer Networks: connect computers around the world – Distributed Systems: software infrastructure atop Comp.Nets– what’s the distinction? well… not precisely defined, but:
• Dist. Systems establish a level of transparency atop Comp.Nets• … of locations, distribution, concurrency, performance…
• A very rough layering may look like this:
6. UC distributed application
2. Nodes i.e. computers (Resources, OS)
1. “Meshing”
distributed system: functionality, services
content/resource distribution
5. communication paradigm4. platform (middleware)
3. optional: overlay network
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
General Introduction – ConnectivityNotes about the “layers” shown on slide before:1. Meshing: how to interconnect adjacent computers
- today: mostly wired; since ~1990: shared switched media- UbiComp: wireless networks crucial
2. Nodes: apart from the mesh, computers are the resources added to system- today: mostly considered homogeneous (except: clients & servers for non-P2P)- today: resources mostly under control of computer owner- UbiComp: very heterogeneous nodes, resources partly ‘socialized’
3. Overlay Network- new: ‘socializes’ (some) resources from layer 2 ubiquitous distributed system- today: only used for special purposes (music exchange etc.)- UbiComp: increasing importance, towards general use
4. Platform: everything beyond 3 providing developers with ‘powerful, easy-to-use’ distr. sys.
- note: layers 3 & 4 use/contain the classical Internet layers TCP/IP etc.- today: 2 major purposes (same for UbiComp, but different (5), different services):
- providing basic services deemed useful for many applications/developers- implementing (5) via special protocols & bookkeeping instances
5. Communication abstraction: crucial for programmers!- today: mainly information pull, client/server paradigm- UbiComp: “push” dominates, but must embrace “pull”, too (see end of chapter)
6. Distributed applications themselves- today: rather ‘closed’ i.e. developed top-down by a team 3
Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Major Connectivity Trends in UC
6. UC distributed application
2. Nodes i.e. computers (Resources, OS)
1. “Meshing”
distributed system: functionality, services
content/resource distribution
5. communication paradigm4. platform (middleware)
3. optional: overlay network
new approach!lean! scalable!
services?
push!more elaborate! inte-gration w/pull, stream
scale!‚everyday‘ humans
& objects
wireless!!easy deployment;
integrating standards?
heterogeneity!federation,resou-rce ‚socialization‘?
Grid & P2P!content /compu-ting distribution?
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Electromagnetic Spectrum
• VLF = Very Low Frequency• LF = Low Frequency• MF = Medium Frequency • HF = High Frequency • VHF = Very High Frequency• UHF = Ultra High Frequency• SHF = Super High Frequency• EHF = Extra High Frequency• UV = Ultraviolet Light
1 Mm300 Hz
10 km30 kHz
100 m3 MHz
1 m300 MHz
10 mm30 GHz
100 µm3 THz
1 µm300 THz
visible lightVLF LF MF HF VHF UHF SHF EHF infrared UV
optical transmissioncoax cabletwisted pair
f * λ = c (c: speed of light, 3* 108 m/s)
note: above figure showsorders-of-magnitude (log)
rules-of-thumb (remember!):1 MHz : 300 m100 MHz : 3 m10 GHz : 3 cm
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
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Basics: 8* „Physics“ Laws & Observations
0. Beginner‘s Confusion don‘t mess up: carrier frequency ↔ bandwidth
1. Playground: electromagnetic spectrum• above FM (e.g. FM-Radio, ~ 108 Hz)• below visible light (~ 1015 Hz) in other words, mobComm uses• ~ microwaves 0.5 - 100 GHz or• ~ infrared > 100 THz
2. Rules-of-Thumb• signal energy ↔ data rate × reach (plus: observe rule 3.1 (-))
related to: electrosmog, advancements in EE, cost• the higher the frequency, the more behavior resembles that of light
– very low frequencies: „surface waves“– medium freq: e.g., reflection at ionosphere ...– very high freq.: „line-of-sight“ (cf. shadowing, distortion... below)
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Basics: 8* „Physics“ Laws & Observations
3. Carrier frequencies move up as R&D continues:
higher carrier frequencies mean ⇒1. (-) needs higher energy, more difficult (expensive) electronics2. (+) fewer competing „networks“ (a mess up to 2 GHz, difficult up to 10) 3. (+) larger bandwidths and/or # of channels ® higher data rates or more subscribers
examples:890 - 915 MHz (1990- today: GSM “uplinks”):5,1 – 5,8 GHz (2000 ff: Wlan 802.11a):59 - 62 GHz (20xx: future WLAN [“MBS”?], WiMax direct links in 50+ GHz)
(notes: 1. WLAN bandwidth still scattered: US 5,15-5,35 / 5,725-5,825,
EU 5,15-5,35 / 5,47-5,725; various [US/EU incompatible] energy leves 2. “MBS” has 3GHz of „space“, GSM uplink just 25 MHz)
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Basics: 8* „Physics“ Laws & Observations
4. Signal attenuation A („path loss“) is crucial• function of distance d, landscape, obstacles (buildings)• single most important difference to wired communications
(most substantial effect on protocol design etc.)!• A simple model for path loss
(A: mean received signal power, related to transmitted power):
– decreases w/ square of frequency
– decreases w/ power-of-α of distance (α = 2 in free space, up to 5 in urban environment)
A = (g: constant)
5. Signal path is crucial• highest attenuation: walls (steel?), signal „shadow“ (urban street?)• buildings reflection multipath distortion, interference !!• line-of-sight multipath: even different network designs!
Pr 1
Ps f2dα= g
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Basics: 8* „Physics“ Laws & Observations
6. Doppler effect mattersmobile sender stretches/quenches waves ® different nets for different mobility speeds?
• slow (walk): WLAN (Laptop), cordless phone• medium (drive): cell phone < 250 km/h ( high-speed trains? need extension!)• fast (fly): airplane phone system...
7. Signal latency often non-issue• in speed-of-light range: 2/3 c (air) ... 1/1 c (in space)• depends (in range above) on altitude (air), frequency, ...• example: GSM 9.6 kbps data, 120B (SMS?) msg. over 3km:
• 10-5 sec latency, 0.1 sec transmission time!
8. Signal latency often crucial (oooops!)• multipath interference (see above)
• timing, synchronization of stations, etc. (see later)
• GPS etc.: calculation of distance, position• High tier antennas, in particular geostationary satellites:
– 35.800 km orbit up + down: some 7*107 m, speed some 3*108 m/s ~ ¼ s delay– 1Mbps link: 120B „put on ether“ in only ~ 10-3 s
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Basics: „Physics“, Observations (6)
• recall attenuation: due to path loss• recall distortion: mainly due to multipath reflection• Further effects:
– shadowing (HiFreq: approaching 100%)– scattering (HiFreq: everyday objects [e.g., 30cm size])– diffraction: adds to attenuation, distortion
Summary of the four „obstacle“ effects
reflection scattering diffractionshadowing
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Basics: SNR, Decibel
„design center“ of all networks (layer 1): Signal-2-Noise-Ratio SNR (or, S/R) i.e. power of ‚signal of interest‘ related to power of ‚what disturbs‘
Decibel: unit used to express relative differences in signal strengths. • given: two signals with powers P1, P2
• compute 10 * log10 (P1/P2)
• e.g.: P1 is 100 times P2:– P1/P2 = 100, log10 (100) = 2, ‚relation P1 : P2‘ is 20 dB
• ‚„relation‘ may be: SNR; power sent vs. received (attenuation); ...• e.g.: signal over 2 hops, no amplifier
– attenuation is 20:1, then 7:1 overall attenuation. is 140:1
– or: 13.01 dB + 8.45 dB = 21.46 dB (10*log1020 + 10*log107 = 10*log10140)
(note: power is f(amplitude2) 20*log10 (A1/A2) yields same result
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Basics: ISI Peculiarities (1)
ISI (InterSymbol Interference) much different from wired networks
1. Hidden-Terminal Problem restricted listen-before-talk (LBT)• given goal: uncoordinated access of N senders to 1 medium • has risk of collision avoid by checking first if medium free• In example:
– S1 & S2 check: LBT o.k.– BUT: R experiences collision
(S2 may also be in „shadow“ of S1)
sender 1
reach (SNR>>0dB)
sender 2
receiver
receiver 1
sender 2
sender 1
receiver 2
2. Exposed-Terminal Problem LBT may be too pessimistic• In example:
– Both S1 and S2 could send– But S2 senses S1 during LBT
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Basics: ISI Peculiarities (2)
ISI (InterSymbol Interference) much different from wired networks
3. Path Loss no listen-while-talk (LWT)• again goal: uncoordinated access of N senders to 1 medium • again: problem collisions detect, resolve• wire (Ethernet): LWT possible
– during Xmit: if signal-on-wire ≠ signal-sent: collision• wireless: LWT impossible (received signal much too low-energy)
4. Path Loss no full duplex traffic• wire (twisted pair): full duplex possible (2 peers use same wire)• wireless: needs two channels (= two carrier frequencies)
– mobile station MS base (transceiver) station BTS: „uplink“– base station mobile station: „downlink“ – (satellite jargon)
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Basics: Cellular Networks
many categorizations of “cell sizes” exist! For our lecture: a) cell sizes (roughly) categorized according to radius, e.g.:
– pico: r = 50 m private (home, office) PicoNet– micro r = 500 m inner city (many users) wLAN, PLMN– macro r = 10 km ‚standard GSM‘; city, road PLMN– hyper r = 30 km rural area PLMN, HALO– overlay r = 200 km high tier antenna coverage HALO, LEO
Satellite
Macro-CellMicro-Cell
UrbanIn-Building
Pico-Cell
Global
Suburban
dik ©
b) categorizationaccording to‘outreach’:
BTS„coverage“ (reach): in reality, odd shape
r
cell
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Basics: Cellular Networks
Roaming (option in cellular networks, some degree always supported):• MS may move freely between cells, even (!) switched-off • MS are “found”, identified upon switch-on (cf. incoming calls)Handover (option in cellular networks):• equals “roaming” during existing connection (active phone call)• connection „hand off“ to new cell• w/o interruption & noticeable effect to user(s)Home location register HLR:• admin. data in „home“ cell of subscriber• holds all permanent data of system-wide concern • may point at „current-VLR“, see belowVisitor location register VLR:• holds all admin. data relevant for the cell in which user „roams“
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Multiple Access: Introduction (2)
• What is divided? ≥ four options (order ≈ tech. complexity):1. Space (SDMA):
• „bands“ are re-used at a certain distance (remote cell)• attenuation remote re-use won‘t interfere (much) with local cell
2. Frequency (FDMA):• different MS use different carrier frequencies• allocated frequency band divided into subbands• GSM900: 124*200kHz, GSM1800: 374*200kHz
3. Time (TDMA): • different MS use different time-slots• often: revolving frames, MS knows „its“ pos. (slot) in frame
4. Code (CDMA):• different MS use different „characteristic“ codes• receiver tunes to this code
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Multiple Access: SDMA-1
• SDMA (SDM): frequency bands re-used in remote cells• different re-use patterns possible:
(repeated) clusters of cells– N = 3, 4, 7 (shown), 12, ... cells per cluster
– each band used only once per cluster
• design parameters:– reuse distance d=f(r,pattern)
– cell radius r (coverage)
• for different N (cluster sizes, patterns):– different d/r ratios different SNR
induced by remote cells of same band
– tradeoff: 1/N of all bands usable per cell
• realistic example (from Book by B. Walke):
1
23
45
6
7
1
23
45
6
7
1
23
45
6
7
1
23
45
6
7
1
23
45
6
7
1
23
45
6
7
1
23
45
6
7
d
d
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Multiple Access: SDMA-2
1. channel assignment:• fixed: each cell has pre-assigned f‘s, for new calls & handover
• reservation: some f‘s reserved for handover• ‚borrowing‘ (from neighbors) ... totally dynamic
2. „Re-use related SNR“ (abstract from other noise)? E.g., N=7: – ...is called C/I ratio (C: carrier signal, I: interference sig.)
– remember path loss L = g⋅f–2⋅d-α (for fixed f: L= h⋅d-α )
– 6 neighbor BTSs w/ distance d (neglect others), max (BTSMS) = r
– see (figures, Pythagoras): d2 = (5⋅(½√3 r))2 + (r+½r)2 = 84/4 r2 = 21r2
– note: i) for carrier signal C: d=r; ii) let α=4; iii) 6 neighbors!
– C/I = (h⋅r-4) / (6⋅h⋅d-4) = d4/6r4 = 212r4/6r4 = 147/2 = 73,5 (18,66dB)
N=3: C/I=13.5=11.3dB (N=4: 16=12dB), but twice as many users possible
r
r
√ r2-¼r2 = ½√3 r
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Multiple Access: FDMA
Example GSM900:
– carrier frequency of uplink/downlink Fu/Fd:
• Fu(n) = 890.2 MHz + (n-1) * 0.2 MHz, n=1 … 124
• Fd(n) = Fu(n) + 45 MHz
note: high-speed (wLAN, wATM etc.) increasing use of OFDM:overlapping bands, orthogonal frequencies (harmonic distances of
subcarriers, equals carrier distance) dyn. bandwidth assignment ...
frequency
time
channel 1
channel 2
channel 3
channel 4
channel 5
optional: gaps for better separationcarrier frequencies
Channels = subbands, distributed over available bandwidth
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Multiple Access: TDMA
• Entire frequency dedicated to single sender-receiver pair, but only for a short period of time (time slot, slice)
• not applicable in analog transmission systems (old telephone net)• e.g., 9.6 kbps per channel > 80 kbps on ether for 8 channels• GSM: 8 slots (TDMA+FDMA!)• practical systems: TDMA always w/ FDMA
frequency
time
C1 C2 C3C0 C4 C5 C6 C7 C0 ........C7
Framesystem data („signaling“) channels = time slots
(1-in-many possible designs)
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Multiple Access: CDMA
CDMA, also called „spread spectrum“ SS• versions: FH (FHSS), DS (DSSS) (chaotic crosstalk, but not ‚concurrent‘!)
• each sender uses “entire” bandwidth & time, „spreads“ code • Wideband (W-CDMA): plus FDMA, but huge subbands (~5MHz)
– Narrow (N-CDMA): smaller (~1MHz), but still >> FDMA+TDMA-subbands
• receiver knows coding rules of sender:– autocorrelations transforms signal back (to lo-bandwidth/hi-power)
– all other signals appear as noise ( # of senders limited, cf. TDM,FDM)
• no channel assignment simpler plus better spectrum utilization used in wireless LANs, increasingly in PLMN
• no synchronization needed (each code is self-synchronizing)• Problem: needs fine-grained transmission power control
– e.g., MSes must adjust such that all signals reach BTS w/ ~same power
– but: signal loss may change very fast (as MS moves)
– IS-95 (USA Qualcomm): 1kbps „adjustment channel“ per MS
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Multiple Access: CDMA (FH)
Frequency-Hopping FH:
• Sender + receiver constantly change (hop-2-new) frequency– basis: pseudo-random sequence, initial value agreed
– origin: military networks (sequence unknown secret comm.)
• „Hope“: few collisions high probability of correction• Fast-FH: several / many hops per bit
– „a few“ collisions per bit don‘t harm
• Slow-FH: several bits per hop– GSM: optional (deterministic) slow-FH
• reason: distribute errors in „noisy“ bands over all channels • hope: corrected by forward-error-correction FEC
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Direct Sequence (by far most commonly used):
• each bit mapped onto sequence of mini-bits (“chips”)• 10 chips / needs 10 times higher data rate (reality: up to ~1000)• Bit „1“ chip-sequence, Bit „0“ inverse sequence• receiver autocorrelates reconstructs original signal
– again: secrecy is by-product (IFF chip-seq. per station is random)SNR near 0 not even existence of communication detectable
– again: much more dynamic than FDM, TDM– plus: no (‚expensive‘) synchronous frequency-hopping needed!
Multiple Access: CDMA (DS)
“0” “1”
Note:in reality,Chip-seq.changesover time
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Concurrent Access: ALOHA
• developed at U Hawaii (islands, hills!) since 1970: – wireless net connects terminals(/hubs) host system
– compares well to: MS BTS
– ‚grand father‘ of concurrent access schemes (wireless and Ethernet)
• channels: 407,350 MHz uplink, 413,475 downlink
– concurrent access (ALOHA) on uplink only
– downlink: packets + acknowledgements (ACK) for uplink packets
• MS send whenever packet ready• BTS sends corresponding ACK on downlink• if 2-or-more MS send with time overlap -> collision
-> BTS ignores „jam“ received -> no ACK
• MSes: timeout (no ACK received) -> send again -> collision repeated? no: since random „backoff“ (waiting time)
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Concurrent Access: Pure ALOHA
• packets 1.1 (station A), 2.1 (B), 3.2 (C) transmitted ok• packets 1.2/3.1 collide, 1.3/2.2 too (partial as bad as total!)
receiptbasestation
total collision partial collisiontime
1.1 2.1 3.2
transmissions
station Apacket transmission time
1.1 1.2 1.3
station B 2.1 2.2
station C 3.1 3.2
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Concurrent Access: Slotted ALOHA
• Fixed (maximum) packet size, equals time slots• common clock for slots (xmitted at downlink latency was rel. low)• start xmit w/ slot only (end ≤ slot end) all collisions are total• ‚surprise‘: mean throughput increased by factor of 2!
– why? xmission slightly later, but ‚just hit‘-overlaps avoided
1.1 1.2 1.3
2.1 2.2
3.1 3.2
station A
station B
station C
transmissions
1 2 3 4 5 6 7 8 9
1.1 2.1 3.21.3 2.2basestation
receipt
total collision
time
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Concurrent Access: CSMA
Idea: stations ‚sense‘ channel before sending– CS = carrier sense („cs = on“ means: channel busy)
– CS also called LBT = listen-before-talk
• advantage: channel busy -> somebody sends -> don‘t disturb• total avoidance of collisions? NO
– MS1 ready2send, MS2 just started (signal has not arrived yet)
-> MS1: CS=off (no ‚busy‘ sensed) -> collision
• collision probability high at end of a transmission:– several MS want to send, sense channel during CS=on
• all MS realize CS=off immediate xmit
– CSMA variants therefore wrt. „when/how to start xmit“
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Concurrent Access: CSMA variantsMajor distinction: procedure applied when station is ready2send1. non-persistent:
snd: while <cs=on> DO < delay (t)> ; /** t constant or random
<send>; /** no polling, no danger after end of Xmit
2. p-persistent: snd: WHILE <cs=on> DO <active wait>; /** usually: cs=off interrupt
IF <random-bool(p)> THEN <send> /** true with probability p < 1 ELSE{ <delay t>; GOTO snd } /** t may be random # of ‚slots‘
/** lower p reduces probability of ‚competition‘ after end of xmission
3. 1-persistent: (the one used for ‘wired’ Ethernet = CSMA/CD – LWT is possible there!) snd: WHILE <cs=on> DO <active wait>; /** as above
<send>; /** high competition backoff algo. IF <collision> THEN { /** here: binary exponential backoff
IF <subsequent-collision> THEN T:=T*T ELSE T:=Tstart; <delay (random(0,T)>; GOTO snd } /** heavy traffic: interval grows exp
time
passive delaynon persistent: S xmits here
activewait
t0 1-persistent:S xmits here p - persistent:
channel busy (cs=on)
station Sready2send
slot
Optional slotting; Reason: slots large enough for ‚cs‘ to reach all stations no collision if other station starts earlier (successful as CSMA/CA) 28
Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Concurrent Access: CSMA/CA
• CA = collision avoidance; several minor variants as described here: ≈ slotted variant of p-persistent CSMA with p=0
• contention window CW = time interval considered collision intensive• after active wait; cs=off delay during IFS (interframe spacing)
– minimum IFS determined by wireless signal latency– 3 different IFSs (signal/priority/data: SIFS, PIFS, DIFS): priorities
• then:– draw random η ∈ [0,1)
– wait for slot that ‚contains‘ time η × CW (active wait: maybe cson)
η -> risk of collision ‚spread‘ over CW
– if still collision -> increase CW exponentially (up to maximum)
• fairness: if preceded by other station, # of slots waited count next time
time
xmit at slot startt0
channel busy
ready2sendIFS
CWdata
η x CW
slots 29
Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©Modulation (1)
Low bandwidth needs highly efficient modulation• known: carrier frequency:
– s(t) = A.sin ( 2πf . t + ϕ )
– bits modulate amplitude A, frequency F,phase ϕ (P)
– A/F/P-„modulation“ AM, FM ...
– also: shift keying ASK, FSK, PSK
– AFP: better, more complex
• QAM: quadrature amplitude modulation= PSK + ASK– e.g., 16 values, 4 bits: I/Q-diagram for 4-QAM
(‚optimal‘ I/Q-diag on 2 amplitude ‚rings‘? or else?)
– 16QAM exists (needs good SNR)(16-PSK would have phases < 2o apart)
– wired-modem 4-QAM example (9600 baud):12 phases, 4 phases w/ 2 amplitudes:
I
Q
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©Modulation (2)
• QPSK (Q=quadrature):– 4 phases: 0, 90, 180, 270 (a)– only phase changes, same amplitude– 2 bits per symbol (dibit)– Problem: 180° phase change -> zero crossing
-> decoding at receiver problematic,because temporarily no carrier
• π/4-QPSK– add 45° phase jump after each symbol,
independent of data– carrier signal always present
• OQPSK: Offset-QPSK– change of real part/imaginary part delayed by
half symbol time– max. phase change reduced to 90°
1100
01
10
11
00
01
10
or: b)a)
I
Q
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Dr. Erwin AitenbichlerProf. Dr. M. Mühlhäuser
Telekooperation©
Modulation (3)
• Advanced FSK: ambiguously called MSK, GMSK (GFSK unambiguous)• Example for M(F)SK below, gaussian filter would make it GFSK
data
even bits
odd bits
1 1 1 1 000
low frequency
highfrequency
MSKsignal
biteven 0 1 0 1odd 0 0 1 1
signal h l l hvalue - - + +
h: high frequencyl: low frequency+: original signal-: inverted signal
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